Step 1 :

After factoring out $ -1 $ we have:

$$ -5x^{2}+141x+4230 = - ~ ( 5x^{2}-141x-4230 ) $$

Step 2 :

Step 2: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 5 , b = -141 ~ \text{ and } ~ c = -4230 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = -4230} $.

$$ a \cdot c = -21150 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -21150 $ and add to $ b = -141 $.

Step 5: All pairs of numbers with a product of $ -21150 $ are:

PRODUCT = -21150
-1     21150	1     -21150
-2     10575	2     -10575
-3     7050	3     -7050
-5     4230	5     -4230
-6     3525	6     -3525
-9     2350	9     -2350
-10     2115	10     -2115
-15     1410	15     -1410
-18     1175	18     -1175
-25     846	25     -846
-30     705	30     -705
-45     470	45     -470
-47     450	47     -450
-50     423	50     -423
-75     282	75     -282
-90     235	90     -235
-94     225	94     -225
-141     150	141     -150

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -141 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -141 }$, we conclude the polynomial cannot be factored.

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